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# Number Theory/Coordinate Geometry.

Question

Coordinate Geometry.
Dear Prof Vijilant

http://en.wikipedia.org/wiki/Analytic_geometry
http://www.mathopenref.com/coordintro.html
http://www.math.com/school/subject3/lessons/S3U1L2GL.html
http://c-schools.net/PPT/Coordinate%20Geometry.ppt
http://www.math.wisc.edu/~robbin/461dir/coordinateGeometry.pdf
http://www.wolframalpha.com/examples/CoordinateGeometry.html

What could be the Impact to different disciplines and applications
of mathematics if Point (x,y) is replaced with Point (y,x).

i.e. x coordinate = Horizontal axis
y coordinate = Vertical axis

Now instead of this standard convention, implement the following
given below

i.e. x coordinate = Vertical axis
y coordinate = Horizontal axis

For examples :

1st Quadrant Point A(3,2) will become Point A(2,3)
2nd Quadrant Point B(-2,3) will become Point B(3,-2)
3rd Quadrant Point C(-3,-4) will become Point C(-4,-3)
4th Quadrant Point D(2,-3) will become Point D(-3,2)

i.e. because the Points are now represented as y,x instead of x,y,
the Plotting of Points A,B,C,D on graph paper will be now different.

Can there be any impact while plotting Graphs viz Sine,Cosine, Tangent waves etc, vector algebra and other applications of mathematics similar to Coordinate Geometry if Point F (x,y) is represented as Point F(y,x) ?

Thanks & Regards,
Prashant S Akerkar

Hello again
In a busy week with many meetings, I haven't time to look up your references.

All it needs is reflection of a graph in the line y = x.  This will not have any affect on definitions of functions, or on identities or theorems.  As long as all occurrences of x and y as algebraic symbols, (which is normally standard as in Word Equations), are in a different font from textual x,y, it would be easy to write a program to change an electronic version of a book from one form to another.  That sounds like a good ICT project.

Regards

vijilant
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Dear Prof Vijilant Thank you. Thanks & Regards, Prashant S Akerkar

Number Theory

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#### Vijilant

##### Expertise

Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.

##### Experience

Teacher of math for 53 years

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AQA Doncaster Bridge Club Danum Strings Orchestra Doncaster Conservative Club Danum Strings Orchestra Simply Voices Choir Doncaster TNS mystery shopping St Paul's Music Group Cantley

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Journal of mathematics and its applications M500 magazine

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BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)

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State Scholarship 1955 Highest Score in Yorkshire on OU course MST209 £50 prize First class honours in OU BA Mathematics

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I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things. One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.